Comments on Enzymes (Chapter 3)

Updated: September 25, 2017Copyright © 2017 John Jechura ([email protected])

Overview Enzymes

Enzymes are biocatalysts – lower activity energy of a reaction by binding with the substrate Proteins, glycoproteins, or RNA

molecules with high molecular weights (15,000 to several million) Some proteins require a nonprotein group as a cofactor

Require optimal conditions (pH, temperature, ionic strength) for maximum activity

Can be used in suspension or in immobilized form Immobilization provides enzyme reutilization w/o recovery & purification May result in diffusion limitations, enzyme instability, loss of activity, and/or

a shift in optimal conditions (pH, ionic strength)

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Issue with enzyme “concentration”

We talk about enzyme concentration but that is a complicated subject Only in highly purified concentrations can be talk about [E] as mol/L or g/L In crude preparations concentration is in terms of “units”

• “Unit” an amount of enzyme that gives a prescribed amount of activity under specified conditions

o For example, one unit would form one µmol product per minute @ specified pH & temperature with substrate concentration much greater than Km

• “Specific activity” is number units per amount of total proteino Concentrating the crude preparation could increase the specific

activityo Only include enzyme that is still catalytically active – concentrating can

denature enzyme & make it inactive

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Enzyme pathways & kinetics

Simplest model is the “lock & key”model

“Saturation” kinetic model formulated Henri and Michaelis & Menten…

Product balance…

Enzyme balance…

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1 2

1

E S ES E Pk k

k

2

PES

dv k

dt

1 1 2 0

ESE S ES ES and E E ES

dk k k

dt



Assume rapid equilibrium for the first step…

From the enzyme balance ([E] = [E0] – [ES])…

From the product balance…

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1

1

E S

ESm

kK

k

0 0E ES S E SES

ES Smm

KK

02 2

P E S SES

S Sm

m m

d Vv k k

dt K K



More general, assume quasi-steady state…

From the enzyme balance ([E] = [E0] – [ES])…

From the product balance…

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1 0 0

2 1 2 1

1

E ES S E SES ES

S

k

k k k kk

2 00

2 2 2 12 1

11

EP E S S

ESS

S

mm

mm

V kd V

v k k k kKdt Kk k

kk

11 1 2

1 2

ES E S0 E S ES ES ES

d kk k k

dt k k


Determining rate parameters for Michaelis-Mentenkinetics

Model parameters Km & Vm to relate v & [S]

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Appropriate for Km from low concentrations

Appropriate for Vm from high concentrations

m

m

V Sv

K S

1 1 1m

m m

Kv V S V

1m

m m

S KS

v V V


More Complicated Enzyme Kinetics

Allosteric enzymes – Have more than one binding site

n is the cooperativity coefficient; n > 1, positive cooperativity Putting into straight-line form…

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S S

S

n

mn

m

d Vv

dt K

S S

S

ln ln S ln

n n

mn

m mm

mm

V vv

V v KK

vn K

V v


More Complicated Enzyme Kinetics – Inhibition

Competition for the enzymes Competitive

• Inhibitor binds with enzyme but is not on a path to create product Noncompetitive

• Binds with sites other than those used by the substrate. • Other reagents needed to block the inhibitor binding.

Uncompetitive• Binds to the ES complex. • Can slow down the overall reaction

Substrate inhibition• Substrate can bind to ES to form a non-productive complex form• Seen at large substrate concentrations

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Competitive inhibition

Competes with the binding of the enzyme but does not lead to product formation. Effect can be overcome with high substrate concentrations

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,app,app

S S1

S1 S

m mm m

mm

V Vv K K

K KK

KI

I

II



Noncompetitive inhibition

Binds with sites other than those used by the substrate. Other reagents needed to block the inhibitor binding.

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,,

,app

S

S11 1

S

m appm mm app

mm

VV Vv V

KKKK II

II



Uncompetitive inhibition

Binds to the ES complex. Reduction of Vm more apparent then the reduction of K´m

12

,

,

,app,app

1 /S1 /

SS1 / 1 /

mmm app

m app

m mmm

VV VKVK

vK KK

KK K

II

I I

II

I I



Substrate inhibition

Low substrate concentrations do not show inhibition, only at larger values

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2

2

Swhen S / 1

SS

when / S 1SSS

1

mSI

mm

mm

mSI

SI

Vv K

KV

v Vv K

KK

K


Comparison of inhibited enzyme kinetics

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Bioprocess Engineering, Basic Concepts, 3rd ed.Shuler, Kargi, & DeLisa, Prentice Hall, 2017


Effect of pH

Some enzymes have ionic groups on their active sites May change the activity of the site May change the overall shape of the

enzyme

Low substrate concentrations do not show inhibition, only at larger values

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2,

, 12

1

HS S1

S HH1 S

H

m mm app m

m app

m

V V Kv K K

K KKK

K


Effect of pH

Some substrates may be ionized

Optimum pH values usually determined experimentally

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1,

,1

S S1

S H1 S

H

m mm app m

m app

m

V V Kv K K

KKK


Temperature effects

Two competing effects Increasing temperature usually will increase the rate coefficients

However, increased temperature could denature the enzyme & lower its activity• There is a time dependency to this

denaturing. Figure 3.15 shows inactivity after being exposed to higher temperatures for 10 minutes.

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2 0 2E and exp /m aV k k A E RT



Insoluble substrate

Mass transfer limited. More potential reactive sites than enzyme molecules

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max,S 2 0max,S

desorb

adsorb

SE

E eqeq

V kV

v kKK

k


Immobilized enzyme systems

Restrict the enzymes within the reactor & not allowing them to leave with the product Enzyme reutilization without

enzyme recovery & purification processes Product purity is usually

improved Minimize effluent handling

problems

Methods Surface immobilization Entrapment

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Immobilized enzyme systems

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Immobilized enzyme systems – surface bound

Diffusional limitations may be significant Damköhler number…

When reaction limited (NDa << 1)

when diffusion limited (NDa >> 1)

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Da

Maximum rate of reactionMaximum rate of diffusion S

m

L b

VN

k

SL bv k

, ,,

S1

S Sm b m

m app m appm app b L b m

V Vv K K

K k K


Immobilized enzyme systems – porous matrix

Now the substrate must diffuse throughthe pathways within the pore Rate of substrate consumption is equal to the

rate across the boundary of the supportparticle

where η is the effectiveness factor

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/3 1 1 and

tanhm m

eff

V KR

D

S

S

Sm S

m S

Vv r

K


Summary

Kinetics of enzyme systems well described by Michaels-Mentonequation form Modification of intrinsic

parameters for various inhibition effects Based on quasi-steady state

assumptions

Inhibition effects Competitive inhibition Noncompetitive inhibition Uncompetitive inhibition Substrate inhibition

Other effects pH Temperature Enzyme concentration

Enzyme immobilization Surface immobilization Entrapment

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Comments on Enzymes (Chapter 3)

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